Divya Tyagi, a Penn State aerospace engineering student, refines a 100-year-old math problem, enhancing wind turbine performance and aerodynamics.
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| Tyagi's groundbreaking work on wind turbine optimization could revolutionize energy efficiency and reduce costs in the renewable energy sector. Image: Penn State |
Pennsylvania, USA — March 28, 2025:
Divya Tyagi, a graduate student in aerospace engineering at Pennsylvania State University, has redefined a century-old mathematical problem, streamlining its structure and expanding its scope for modern aerodynamics, according to a Penn State post.
Tyagi added a new layer to a problem first proposed by British aerodynamicist Hermann Glauert, developing a novel approach to optimize wind turbine performance. Her research, which began as an undergraduate thesis at Penn State’s Schreyer Honors College, was published in Wind Energy Science.
The focus of her work is determining the ideal aerodynamic conditions that maximize wind turbine power output. While Glauert’s original model only considered the maximum attainable power coefficient—a measure of turbine efficiency—Tyagi’s enhancement also factors in the total force and moment coefficients acting on the rotor, including the bending of turbine blades under wind pressure.
Sven Schmitz, a professor of aerospace engineering and co-author of the paper, noted that Glauert’s work did not account for downwind thrust forces or the structural loads placed on turbine blades. Tyagi’s revised approach, using the calculus of variations, provides a more comprehensive mathematical framework, offering researchers and engineers the tools to explore new areas of wind turbine design. Schmitz believes her findings will influence the next generation of wind turbines and could be integrated into engineering courses around the world.
Tyagi views her research as a step toward greater wind energy efficiency and lower operational costs. She explained that even a 1% increase in a turbine's power coefficient could lead to substantial energy gains, potentially powering an entire neighborhood. Her groundbreaking work earned her the Anthony E. Wolk Award for the best undergraduate aerospace engineering thesis at Penn State.